Approximation of multi-parametric functions using the differential polynomial neural network.

*(English)*Zbl 1372.68228Summary: Unknown data relations can describe a lot of complex systems through a partial differential equation solution of a multi-parametric function approximation. Common artificial neural network techniques of a pattern classification or function approximation in general are based on whole-pattern similarity relations of trained and tested data samples. It applies input variables of only absolute interval values, which may cause problems by far various training and testing data ranges. Differential polynomial neural network is a new type of neural network developed by the author, which constructs and resolves an unknown general partial differential equation, describing a system model of dependent variables. It creates a sum of fractional polynomial terms, defining partial mutual derivative changes of input variables combinations. This type of regression is based on learned generalized data relations. It might improve dynamic system models a standard time-series prediction, as the character of relative data allows to apply a wider range of input interval values than defined by the trained data. Also the characteristics of differential equation solutions facilitate a great variety of model forms.

##### MSC:

68T05 | Learning and adaptive systems in artificial intelligence |

35Q68 | PDEs in connection with computer science |

##### Keywords:

polynomial neural network; data relations; partial differential equation construction; multi-parametric function approximation; sum derivative term
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\textit{L. Zjavka}, Math. Sci., Springer 7, Paper No. 33, 7 p. (2013; Zbl 1372.68228)

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##### References:

[1] | Zhou, B; Xiao-Li, Y; Liu, R; Wei, W, Image segmentation with partial differential equations, Information Technology Journal, 9, 1049-1052, (2010) |

[2] | Iba H: Inference of differential equation models by genetic programming. : Information Sciences, Volume 178, Issue 23, 1 December 2008, Pages; 2008:4453-4468. |

[3] | Tsoulos, I; Gavrilis, D; Glavas, E, Solving differential equations with constructed neural networks neurocomputing, volume: 72, Issues, 10-12, 2385-2391, (2009) |

[4] | Giles, CL, Noisy time series prediction using recurrent neural networks and grammatical inference, Machine Learning, 44, 161-183, (2001) · Zbl 0983.68163 |

[5] | Zjavka, L, Recognition of generalized patterns by a differential polynomial neural network, ETASR - Engineering, Technology & Applied Science Research, 2, 167-172, (2012) |

[6] | Ivakhnenko AG: Polynomial theory of complex systems. : IEEE Transactions on systems, Vol. SMC-1, No.4; 1971. |

[7] | Nikolaev NY, Iba H: Adaptive Learning of Polynomial Networks. New York: Springer; 2006. · Zbl 1119.68158 |

[8] | Kuneš J, Vavroch O, Franta V: Fundamentals of modeling. in Czech: SNTL Praha; 1989. |

[9] | Das S, Abraham A, Konar A: Particle swarm optimization and Differential evolution algorithms. Springer-Verlag Berlin: Studies in Computational Intelligence 116, 1-38; 2008. |

[10] | Kluvánek I, Mišík L, Svec M, Matematics I: SNTL Bratislava. in Slovak: ; 1966. |

[11] | Obitko M: Genetic algorithms. Hochshule fur Technik und Wirtschaft Dresden; 1998. [Online] Available: http://www.obitko.com/tutorials/genetic-algorithms/ |

[12] | Nikolaev, NY; Iba, H, Polynomial harmonic GMDH learning networks for time series modeling, Neural Networks, 16, 1527-1540, (2003) |

[13] | Zjavka L: Construction and adjustment of differential polynomial neural network. Academic Journals: Journal of Engineering and Computer Innovations Vol. 2 Num. 3, March 2011; 2011:40-50. |

[14] | Galkin I: Polynomial neural networks. Materials for UML 91. University Mass Lowell: 531 Data mining course; http://ulcar.uml.edu/ iag/CS/Polynomial-NN.html |

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